The impedance boundary value problem for the time harmonic Maxwell equations

1981 ◽  
Vol 3 (1) ◽  
pp. 475-487 ◽  
Author(s):  
D. Colton ◽  
R. Kress ◽  
G. C. Hsiao
Keyword(s):  
Boundary Value Problem ◽  
Maxwell Equations ◽  
Boundary Value ◽  
Impedance Boundary ◽  
Time Harmonic

scholarly journals The Riemann boundary value problem related to the time-harmonic Maxwell equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Pei Yang ◽  
Liping Wang ◽  
Zuoliang Xu
Keyword(s):  
Boundary Value Problem ◽  
Maxwell Equations ◽  
Boundary Value ◽  
Uniform Boundedness ◽  
Matrix Operator ◽  
Cauchy Type ◽  
Riemann Boundary Value Problem ◽  
Riemann Boundary ◽  
Time Harmonic ◽  
Definition Of

AbstractIn this paper, we first give the definition of Teodorescu operator related to the $\mathcal{N}$ N matrix operator and discuss a series of properties of this operator, such as uniform boundedness, Hölder continuity and so on. Then we propose the Riemann boundary value problem related to the $\mathcal{N}$ N matrix operator. Finally, using the intimate relationship of the corresponding Cauchy-type integral between the $\mathcal{N}$ N matrix operator and the time-harmonic Maxwell equations, we investigate the Riemann boundary value problem related to the time-harmonic Maxwell equations and obtain the integral representation of the solution.

scholarly journals RELAXATION APPROXIMATION OF THE KERR MODEL FOR THE THREE-DIMENSIONAL INITIAL-BOUNDARY VALUE PROBLEM

2009 ◽  
Vol 06 (03) ◽  
pp. 577-614 ◽  
Author(s):  
GILLES CARBOU ◽  
BERNARD HANOUZET
Keyword(s):  
Boundary Value Problem ◽  
Response Time ◽  
Boundary Value ◽  
Three Dimensional ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Debye Model ◽  
Impedance Boundary Condition ◽  
Impedance Boundary ◽  
Initial Boundary Value

The electromagnetic wave propagation in a nonlinear medium is described by the Kerr model in the case of an instantaneous response of the material, or by the Kerr–Debye model if the material exhibits a finite response time. Both models are quasilinear hyperbolic and are endowed with a dissipative entropy. The initial-boundary value problem with a maximal-dissipative impedance boundary condition is considered here. When the response time is fixed, in both the one-dimensional and two-dimensional transverse electric cases, the global existence of smooth solutions for the Kerr–Debye system is established. When the response time tends to zero, the convergence of the Kerr–Debye model to the Kerr model is established in the general case, i.e. the Kerr model is the zero relaxation limit of the Kerr–Debye model.

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